Remainder when x^{3}-a x^{2}+6 x-a is divided by x-a .

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2. Polynomials

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Find the remainder when $x^{3}-a x^{2}+6 x-a$ is divided by $x-a$.

A

$6x-a$

B

$6a$

C

$5a$

D

$5$

Solution

We have $p ( x )= x ^{3}- ax ^{2}+6 x – a$

$\because $ Zero of $x – a$ is $a$. $[\because x-a=0 \Rightarrow x=a]$

$\therefore $ $p ( a )=( a )^{3}- a ( a )^{2}+6( a )- a = a ^{3}- a ^{3}+6 a – a =0+5 a =5 a$

Thus, the required remainder $=5 a$

Standard 9

Mathematics

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